Batting for baseball's highest-paid player, Ibanez homered to right-center with one out in the ninth inning off major league saves leader Jim Johnson to tie it at 2. He then hit the first pitch from Brian Matusz leading off the 12th.
Phil Hughes will start for the Yankees on Thursday night in Game 4 of the best-of-five series. Chris Tillman or Joe Saunders will start for Baltimore.
Baltimore had won 16 straight extra-inning games, and had been 76-0 when leading after seven, before the Yankees stung them.
"It was a great experience. We do it as a team. We stay after it," Ibanez said.
Ibanez got that chance after Yankees manager Joe Girardi made the decision to bat for Rodriguez -- the first time A-Rod had ever been pinch-hit for in a postseason game, according to STATS LLC.
Rodriguez has 647 career home runs -- he's chasing the all-time record of 762 by Barry Bonds -- but was just 1 for 12 with no RBIs and seven strikeouts in this series when Girardi pulled him.
The brash, young Orioles appeared poised to move within a game of their first trip to the AL championship series since 1997.
But Ibanez hit a 1-0 pitch into the seats, setting off a raucous celebration in what had been a demoralized Yankee Stadium crowd. Rodriguez led the cheers, raising an arm in the dugout and high-fiving injured star Mariano Rivera.
Now the Yankees could put away the Orioles for good.
After their 10-game July lead was cut to zero in early September, the Yankees repelled every Orioles charge. The teams were tied 10 times in the final month but New York ended up atop the division.
New York won the opener in Baltimore scoring five runs in the ninth off Johnson. The Orioles won Game 2 and rode Miguel Gonzalez's pretty performance to a 2-1 lead in the ninth.
But The Yankees limited Baltimore to one hit after Manny Machado homered in the fifth. Ryan Flaherty homered earlier for the Orioles.
Robert Andino was doubled off second after leading off the ninth with a single and advancing on a sacrifice.
Boone Logan got one out in relief of Hiroki Kuroda, who gave up two solo homers in 8 1-3 innings. Closer Rafael Soriano pitched 1 1-3 innings and David Robertson went two, finishing off his outing by bumping into and tagging Andino to end the top of the 12th.
Derek Jeter tied the score with an RBI triple in the third for the Yankees. Jeter, limping because of a sore ankle, came out after eight innings.